Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
472 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×#19151414 | C2 | semidirect |
| 5. #26018350 | C2 | semidirect |
| 6. #26018332 | C2 | semidirect |
| 7. C89×#1971 | C2 | semidirect |
| 12. C2×#15667958 | C4 | semidirect |
| 13. C2×#15667955 | C4 | semidirect |
| 174. #1971 | D89 | semidirect |
| 177. C89 | #13039 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152039 | 2 |
| C2×#19151721 | 2 |
| C2×#19151414 | 2 |
| C2×#19151407 | 2 |
| #26018350 | 2 |
| #26018332 | 2 |
| C89×#1971 | 2 |
| #13039 | 89 |